Economic design of two-stage control charts with skewed and dependent measurements

In many instances, the cost is high to monitor primary quality characteristic called performance variable, but it could be more economical to monitor its surrogate. To cover asymmetric processes in an alternating fashion of two-stage charting design using either performance variable or surrogate variable, both process variables are modeled by a skew normal distribution, respectively. The proposed two-stage control charts are constructed with an economic viewpoint using Markov chain approach. Two algorithms are provided to implement the proposed charting method. The application of the proposed charting method and its advantages over the existing methods are presented through an illustrating example.